Gauged linear sigma model with F-term for A-type ALE space

We construct yet another N=(4,4) gauged linear sigma model for the A_N-type ALE space. In our construction the toric data of the ALE space are manifest. Due to the SU(2)_R symmetry, the F-term is automatically determined. The toric data, which govern the Kähler structures of the ALE space, are embedded into U(1) charges of charged hypermultiplets. The F-term is also necessary to determine the complex structures of the ALE space. In the IR limit, we obtain the Kähler potential of the A_N-type ALE space. We also find the origin of the ℤ_N+1 orbifold symmetry in the singular limit of the A_N-type ALE space. In a special case, we reproduce an explicit form of the Kähler potential of the A₁-type ALE space, i.e., the Eguchi–Hanson space